
Notice that we explicitly condition on \(f\) , which is the operator \({\theta }\mapsto f_{{\theta }}\) , even if this is not stochastic; this choice will simplify notation at a later stage.
Mimicking the standard autoencoder reconstruction loss, we set \(p(\mathbf {x}_{\text{rec}}|{\theta },\mathbf {x},f)\!=\!\mathcal {N}(\mathbf {x}_{\text{rec}}|f_{\theta }(x),\mathbb {I})\) . Since \(p({\theta }|\mathbf {x},f)\)  is unknown, the reconstruction likelihood (REF ) is intractable, and approximations are in order. Similar to [1]}, we resort to a Gaussian approximation, but rather than learning the variance variationally, we opt for la. This will allow us to sample nns and deduce uncertainties in both latent and output space as illustrated in fig:overview.
